tailieunhanh - PHYSICS AND FRACTAL STRUCTURES

The end of the 1970s saw the idea of fractal geometry spread into numerous areas of physics. Indeed, the concept of fractal geometry, introduced by B. Mandelbrot, provides a solid framework for the analysis of natural phenomena in various scientific domains. As Roger Pynn wrote in Nature, “If this opinion continues to spread, we won’t have to wait long before the study of fractals becomes an obligatory part of the university curriculum.” | JearvFran ois Gouyet Physics and Fractal Structures PHYSICS AND FRACTAL STRUCTURES . GOUYET Laboratoire de Physique de la Matière Condensée Ecole Polytechnique Foreword When intellectual and political movements ponder their roots no event looms larger than the first congress. The first meeting on fractals was held in July 1982 in Courchevel in the French Alps through the initiative of Herbert Budd and with the support of IBM Europe Institute. Jean-Franẹois Gouyet s book reminds me of Courchevel because it was there that I made the acquaintance and sealed the friendship of one of the participants Bernard Sapoval and it was from there that the fractal bug was taken to Ecole Polytechnique. Sapoval Gouyet and Michel Rosso soon undertook the work that made their laboratory an internationally recognized center for fractal research. If I am recounting all this it is to underline that Gouyet is not merely the author of a new textbook but an active player on a world-famous stage. While the tone is straightforward as befits a textbook he speaks with authority and deserves to be heard. The topic of fractal diffusion fronts which brought great renown to Gouyet and his colleagues at Polytechnique is hard to classify so numerous and varied are the fields to which it applies. I find this feature to be particularly attractive. The discovery of fractal diffusion fronts can indeed be said to concern the theory of welding where it found its original motivation. But it can also be said to concern the physics of poorly condensed matter. Finally it also concerns one of the most fundamental concepts of mathematics namely diffusion. Ever since the time of Fourier and then of Bachelier 1900 and Wiener 1922 the study of diffusion keeps moving forward yet entirely new questions come about rarely. Diffusion fronts brought in something entirely new. Returning to the book itself if the variety of the topics comes as a surprise to the reader and if the brevity of some of treatments leaves .